The powered turret had its origins in the very early 1930s when it became apparent to the RAF that the accuracy of its gunners in open mounts was dropping off. The problem was increased aircraft speeds of 1930s aircraft produced greater slipstream effects especially for gunners in the nose and / or where they were required to stand to fire downwards. So the answer became to provide an enclosure to protect the gunner from slipstream. But in these early turrets while turret rotation was powered by various means (the Overstrand turret was pneumatic, other chose slipstream driven props, an early Armstrong Whitworth turret was powered by the gunners feet before we get to hydraulics or electric) the gun itself was still operated manually, and still only had the ring and bead sight.
A few more years had to pass before powered rotation and elevation became the norm. One of the first of these was the Bristol B.I installed in the Blenheim (deliveries from March 1937).
Boulton Paul designs after the Overstrand turret switched to hydraulic power and exploited technology born in France where the Armee de l'Air had shown no interest in it. Two French built prototypes arrived in 1937 for tests. A&AEE tests on one were protracted, and it was only in 1938 that it was returned to BP for installation in the second prototype Defiant. From there BP developed a range of turrets for various aircraft. Development timescales were similar in other companies.
The downside of powered turrets was weight and complexity especially if they still only contained a single Vickers K gun with their pan magazines. As things developed gun multiplied and ammo chutes etc to supply them were added.
If your only intention is to protect gunners from slipstream effects, there are easier ways to do it than turrets. See He111 for example, or the B-17C/D.
So development of the BP Defiant with its 4 gun turret was started before even the likes of the Blenheim with its early single gun powered turret had entered service. Like many designs of that era its development became protracted.